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Geometry Ch3.6 #11 Solution

Question from Anna:

Geometry Chapter 3 Lesson 5 Number 11. How do we figure this out?

Answer from Cassidy Cash:

Start with what we know:

North East West South make 90-degree angles so <NOE = <EOS = <SOW = 90 degrees

A = 50. So to this point, draw with N = 0, A = 50 (given), E = 90, S = 180, W = 270

Now you have to figure out the rest. Here are a few ways.

  1. You know <NOE = 50 = <DOS since these are linear pairs. So add 50 to the 180 to get 230 at point D. Keep doing the vertical angles.
  2. Or you also know the lines of the map (north, east, south, west) bisect those angles < AOB and the like. So If <NOA = 50 and you know <NOE = 90 so <AOE = 40. And since they bisect, you now know <EOB=40, <BOS=50.

Either route you take, you just will see a pattern and you start figuring out one from the other.

So in the end the coordinates (angles) are 0,50,90, 130,180,230,270, and 310